Why is rotation about the bond axis possible for single-bonded atoms but not double-bonded atoms?

The mixing of two atomic orbitals to form a new hybrid orbital is referred to as hybridization and the orbitals that are formed are called hybrid orbitals.

The end-to-end overlap between s, p, and hybrid atomic orbitals leads to sigma bonds, one with electron density distributed symmetrically along the bond axis. Side-to-side overlap of p-p orbitals or p-d orbitals leads to pi bond, one with electron density distributed above and below the bond axis. A double consists of one sigma bond and one pi bond, whereas a single bond consists of only one sigma bond. Since the pi bond is formed due to side-on overlapping, movement along the bond axis is restricted.

If rotation of a single-bonded atom is done about the bond axis, then - since electron density is symmetrically distributed along the bond axis - hence the bond will not break. But for a double bond, if rotation is carried along the bond axis, it will break as electron density is distributed above and below the bond axis. Hence rotation about the bond axis is possible for single-bonded atoms, but not for double-bonded atoms.